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Let's solve the problem step by step.

### Problem a:
We need to find the coordinates of the points of intersection for the following equations:
\[
x^2 + y^2 = 4
\]
\[
x = 2
\]

#### Step 1: Substitute \( x = 2 \) into the equation \( x^2 + y^2 = 4 \).

\[
2^2 + y^2 = 4
\]
\[
4 + y^2 = 4
\]
\[
y^2 = 0
\]
\[
y = 0
\]

#### Step 2: Write down the coordinates.
The only point of intersection is when \( x = 2 \) and \( y = 0 \), so the coordinates are \( (2, 0) \).

Would you like to go over the details of this solution or explore the other parts of the question?

Here are 5 related questions:
1. How do you solve a system of equations involving a circle and a line?
2. What is the geometric interpretation of solving \( x^2 + y^2 = r^2 \) with \( x = a \)?
3. How can you find the intersection points of a parabola and a line?
4. How would the solution change if the radius of the circle was larger?
5. What if the line was not vertical but had a different slope?

**Tip:** When dealing with intersection problems, always start by substituting one equation into the other to reduce the number of variables.

Find the coordinates of the points of intersection of x^2 + y^2 = 4 and x = 2.

Learn how to find the intersection points of a circle with the equation x^2 + y^2 = 4 and the vertical line x = 2. Detailed steps include substituting the value of x and solving for y. Suitable for students in Grades 9-12.

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